The Gunners will return to action on Saturday evening when they take on City away from home at the Etihad Stadium in the Premier League.
Tierney was told to quarantine himself for 14 days last Tuesday after his Scotland international teammate Stuart Armstrong tested positive for coronavirus.
The 23-year-old left-back was deemed a close contact of the Southampton midfielder despite the former Celtic defender maintaining social distance from him.
Arteta has said that he hopes that Tierney is able to play for his side against City this weekend.
The Spaniard told Arsenal’s official website about Tierney: “This is getting very complicated when we are sending players abroad and obviously you lose control, some authorities have different regulations to the actual ones in the Premier League.
“We are still having some discussions with the authorities and hopefully we will know more this afternoon.”
When asked whether Tierney could play this weekend, Arteta said: “I hope so.”
Arsenal are fourth in the Premier League table at the moment with nine points from four matches.
Meanwhile, City currently find themselves 14th in the standings with four points from three matches.